Tip Vortex Formation and Evolution to the Near Wake of a Rotor in ...

Tip Vortex Formation and Evolution to the Near Wake of a Rotor in Forward FlightOliver D. Wonggt5071c@prism.gatech.eduNarayanan M. Komerathnarayanan.komerath@ae.gatech.eduSchool of Aerospace EngineeringGeorgia Institute of TechnologyAtlanta, GA 30332Realistic models of the formation, structure and evolution of tip vortices are essential to predict rotor bladeaeroacoustics. Velocity measurements are reported here on tip vortex formation and evolution to the near wake froma teetering, untwisted, square-tipped, two-bladed NACA0015 rotor in low-speed forward flight. Given assuredperiodicity and appropriate measurement techniques, vortex formation results confirm observations made in the1980s. Circumferential velocity profiles are observed as early as x/c = 0.47, growing in strength and core radius upto x/c of 1.06. The profiles of circumferential velocity manifest the rollup of discrete vortex filaments. The effect ofseed particle dynamics on the accuracy of vortex measurements in the near wake is studied to verify accuracy. Thewake structure and the tip vortex properties up to 488° of wake age are presented. Harmonic variations are seen inthe tip vortex core axial velocity. A strong spanwise velocity is seen on the pressure and suction sides of the blade.The core axial velocity appears to approach tip speed at origin, and the core circumferential velocity remainsconstant for a large distance after formation. The equations of motion describing seed particle motion in a 2D vortexwere numerically integrated to quantify the velocity error of LDV measurements of the near-wake vortexcharacteristics due to seed particle dynamics. For a vortex strength of 0.75 m 2 /s typical of rotor tests at a tip Machnumber of 0.15, the error in circumferential velocity error due to lag of particles between 1 and 5µm, is seen to havean upper bound of 2%.I. IntroductionThe rotor blade tip vortex is perhaps the most prominentand critical aspect of rotorcraft aerodynamics andaeroacoustics. Yet there is substantial uncertainty todayabout the precise manner of its origin, structure andevolution. In this paper, we study these aspects usingthe vortex trailed from the tip of a NACA 0015 rotorblade at 10 degrees collective pitch in a wind tunnel.This paper deals with two aspects. The first is todescribe measurements of the velocity field surroundingthe blade-tip. These data, along with previousmeasurements of the tip-vortex properties in the nearwake, complete a dataset describing the vortex frominception through evolution in the near wake [1-2]. Thesecond aspect is the velocity error in measurement ofthe near-wake vortex properties due to seed particledynamics. Laser velocimetry (LV) measures thevelocity of seed particles convected by the flow toascertain the fluid velocity. However, particles entrainedin vortices are subject to centrifugal forces from rotationof the fluid. To determine the accuracy of themeasurements of the tip-vortex characteristics in thenear-wake, it is necessary to quantify the errorintroduced by the centrifugal force.II. Previous WorkII.1 Previous work on tip vortex velocity fieldsThompson et al [3] used LV to examine the formationprocess as well as the vortex properties in the near-wakeof a single-bladed rotor in the Georgia Tech 9-foothover facility in the mid-1980s. In this facility, a wakeinductor refined by trial and error enabled rotoroperation over a specified range of test conditions withthe problems of vortex impingement on facility walls.Under these conditions, rotor-synchronized laser sheetvisualization howed that the vortex followed aprecisely-repeating trajectory for at least the first 360degrees and probably the first 540 degrees of vortexage. Using mineral oil seeding which showed some“spinout” (discussed later in this paper), they sliced thewake radially using an argon ion laser sheet,approximately 1mm thick, and strobed the laser beamusing a chopper wheel driven on a motor synchronizedto the rotor shaft. The rotor was operated at 600rpm. A35 mm camera set on long exposure captured the vortexcores clearly for at least the first 3 turns. Aperiodicity(jitter) of even one core radius would have moved thebrightest regions of the photograph (the heavily-seededregion at the edge of the core) across the darkest regionthe core center, smearing out the photos. Withperiodicity thus assured, they used sub-micron particlesof incense smoke to seed the core of the tip vortex, andmeasured each of the 3 components of velocity, in turn,across the vortex using a specially-designed Remote-Aligned Off-Axis Receiver [4]. With this arrangement,they obtained fairly uniform seed particle arrival ratesacross the entire tip vortex. They found that duringformation, the vortex achieved its maximum strength ata x/c of 0.5 and 0.6 for C T values of 0.0057 and 0.0022Copyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

espectively. Thompson also observed secondaryfeatures in the circumferential velocity profiles for earlywake ages. These were not understood at the time; atpresent we postulate that these are a manifestation of therollup of discrete vortical filaments during the formationof the tip vortex. However, Thompson’s flowvisualization and measurements showed that the tipvortex of a rotor does persist with much of its initialstrength for large vortex ages.Brand et al [5,6] and Liou et al [7-9] examined vortextrajectories and dynamics of the two-bladed rotor usedin the present paper, in forward flight in the same windtunnel. They showed, again, that vortex trajectoriesrepeated with precise periodicity, provided wakeimpingement on the tunnel floor, and wakerecirculation, were prevented by going to sufficientlyhigh advance ratio (>0.06 in this experimentalconfiguration). Again, the vortex was seen to maintainmuch of its initial strength for vortex ages over 400degrees, which was the limit of their interest becausethey were studying rotor vortex/airframe interaction.Komerath et al [10] extended the single-bladed rotorwith a double-swept blade tip in the 9-foot hover facilityat Georgia Tech to study effects at high pitch angles.During their experiments, they observed that at certainconditions, the tip vortices impinged on the edge of thewake inductor and recirculated in the facility: this wasassociated with the development of severe aperiodicjitter of the vortex trajectories.Funk et al [11] conducted extensive measurements ofthe flowfield between the 2-bladed rotor and a wing inthe John Harper wind tunnel. Although vortextrajectories were substantially altered by winginteraction, the results on periodic repeatability ofvortex locations, and persistence of vortices to largeages, both remained unchanged.Carradonna et al [12,13] visualized the wake of a 2-bladed rotor in axial climb in the 30’x30’ SettlingChamber of the 7’x 10’ wind tunnel at Ames ResearchCenter. Again they found that when wake recirculationwas prevented, the vortex trajectories repeated quiteperfectly from cycle to cycle of blade motion, even asthe climb velocity was brought towards zero. Vortexcores were discernible by the seed particle patterns forseveral turns of the vortex, until merger betweenvortices smeared the patterns. From the above, it is quiteclear that the tip vortex of a rotor persists over longvortex ages. Also, aperiodic “jitter” of vortices is not abasic fluid mechanical feature of rotor wakes, providedrecirculation is avoided.McAlister [14-15] studied the velocity field in the nearwake of a two-bladed rotor in hover using a 3-component laser velocimeter. The test conditions were aC t of 0.005 at 1100 and 550 RPM. He found that threechords downstream of the blade the vortex meander wasless than one core diameter. The meander increased byan order of magnitude by the time vortex reached 180°of vortex age. He also noted that changing the rotationalspeed did not have an effect on the core diameter, thegeneral appearance of the trailing vortex, or themagnitude of the velocity components relative to thetip-speed.In the late 1990s, measurements were reported byLeishman et al [16] using a single-bladed rotor in ahover facility, using a 3-component laser velocimeter.These measurements indicated rapid “diffusion” of thetip vortices within the first 90 degrees of vortex age.Substantial aperiodicity was observed. Thesephenomena were attributed to turbulence in the core,and the rapid smearing of the vortex velocity profiledata was described as turbulent diffusion [16]. Howeverthe data acquisition procedures used had taken noaccount of aperiodicity, raising the possibility thatvortex profile data, averaged over several cycles, hadbecome severely smeared by cycle-to-cycle uncertaintyin vortex position. Conlisk et al [17] showed byanalytical arguments based on orders of magnitude thatturbulent diffusion was not a plausible explanation forvortex decay of the rate reported in Ref. [16].Mahalingam et al [18-20] conducted measurements onthe advancing blade side (ABS) of the two-bladed rotorused in this paper, in low-speed forward flight. Heshowed by flow visualization and LDV measurementsthat the rotor flow field was periodic to better than 1° ofrotor azimuth at an advance ratios 0.1. Havingestablished periodicity to ensure the quality of the data,he studied the near-blade flowfield as well as the nearwake. In these measurements, he observed strongspanwise velocities directed towards the blade-tip onboth the suction and pressure sides of the blade. Thevelocities approached 40% of the tip-speed on thepressure side. Spanwise flow on the suction side wasmuch lower. Mahalingam also observed secondaryeffects in the circumferential velocity profiles duringformation. He showed that the turbulence level insidethe core was lower than that in the freestream, as mightbe expected in a region of favorable pressure gradient.Both the vortex strength and the axial velocity in thecore were shown to persist out to more than 500 degreesof vortex age.II.2 Previous Work on Seed Particle InertiaAs previously mentioned, velocity measurementtechniques that rely on seed particles carried by a fluidCopyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

are subject to errors due to finite particle inertia. In thecase of laser velocimetry, the experimenter faces adilemma: light scattering from particles smaller than 1micron is generally difficult to capture accurately in thebackscatter mode (light captured at the same lens whichis used to transmit the laser beams) over the largedistances used for laser velocimetry in rotor facilities.Particles larger than one micron are believed toexperience substantial centrifugal drift with respect tothe flow in the core of a tip vortex. Thompson et al[3,4]dealt with this problem by developing an Off-AxisScatter Receiver [4]. This device could be alignedremotely to stay focused on the measurement volume asit was traversed across a large facility, and capturescattering from sub-micron particles. This is howeverless convenient than using a backscatter LV system, andis difficult when the rotor is near other objects whichblock the line of sight.It is therefore necessary to use larger particles, andquantify the error due to particle spinout. Dring et al[21] has examined the trajectories of particles in turbinecascades. He concluded that the Stokes number (St) hadthe greatest influence on particle behavior. Furthermore,he determined that particles with St ≤ 0.1 would veryclosely follow the streamlines and particles with St > 10would be centrifuged across streamlines. In anotherstudy, Dring [22] integrated the equations of motion forparticles in several flows to provide guidance on LVseed particle size selection. The flows included a turbinecascade, a step deceleration and exponential andsinusoidal accelerations. He determined that the Stokesnumber required to achieve 1% accuracy depended onthe type of flow. In a turbine cascade, he found that aStokes number of less than 0.01 was required, but in asinusoidal flow 0.14 was tolerable.Dring, et al [23] and Kriebel [24] examined the behaviorof particles in centrifugal particle separators. In theseflows, the gas experiences solid body rotation. This isanalogous to vortex core velocity profiles, except thatthe strong axial velocity is absent. Dring’s analysisassumed that the particle and gas velocity were equal.He also used several drag models instead of assumingthat Stokes relation holds. Dring [23] asserts: “axialvelocities do not alter the solution so long as theparticle and fluid axial velocities are equal andconstant.” Kriebel’s study did not place anyassumptions on the particle and fluid velocity. However,he used Stokes relation to estimate drag acting on theparticle. Comparison with experimental data is alsoprovided. Neither of these analyses is valid in thepotential velocity region outside the vortex core.Leishman [25] calculated the behavior of seed particlesin a “desingularized” vortex. His study used particlesranging from 0.5 to 2.0 µm and a vortex circulation of5.6 m 2 s -1 . Inside the vortex core, he predicted velocityerrors as high as 10% and 25% for the tangential andradial velocities, respectively, for the 2 µm particle. Thesmaller particles resulted in lower errors. His study alsoexamined particle count distribution. The highestparticle distributions occurred at r/R c of 1.7 for the0.5µm particles, 2.6 for the 1.0µm particles and 3.8 forthe 2.0µm particles. Although intended for rotor tipvortex applications, this work did not consider theeffects of the strong axial velocity in the core. It shouldbe noted here that the vortex strengths used byLeishman [25] are almost 5 times those encountered inthe present rotor flowfield.The previous work on seed particle inertia has beenfocused on 2-dimensional models of vortices. In therotor tip vortex core, as shown by Refs. [3-14], there is avery substantial axial velocity. The resulting sink-likeeffects on the flowfield should cause an inward-directedradial fluid velocity, which should considerably inhibitthe drift of particles out of the middle of the core, wherethe centrifugal acceleration is much lower than at thecore edge. Considering experimental results obtained atthe present authors’ laboratory with cleanly-periodic,well-resolve vortices, it is evident that the estimates ofseed-particle inertia error cited, for example, in [25]convey an overconservative picture. This issue needs tobe considered, and upper bounds are sought for thesetypes of errors.III. Issues and objectives of present workIn the present work, the flowfield near the blade tip ismeasured, to examine the development of the tip vortex.These measurements are then related to measurementsof the vortex in the wake. Mineral oil seeding is used.The dynamics of the seed particles are examined in thecontext of velocity field error, and the observedevacuation of particles from the vortex core as vortexage increases. Issues are:1.What are observed differences of rotor tip vortexcores from fixed-wing vortex cores?2. What is the nature of the nascent core?3. How does the vortex circulation change as the vortexdevelops over the blade tip?4. Are the predictions of error due to particle spin-outvalid for rotor tip vortices?5. Why does the vortex core become clear of seedparticles further downstream?6. What are the implications for the evolution of thevortex further downstream in the wake?The objective of the paper is to resolve thecontradictions seen in the literature regarding the aboveissues. It is noted that the results given here are limitedto the incompressible flow regime. The blade used has aCopyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

square tip and is heavily tip-loaded due to the constantchord,rectangular planform. The Reynolds number ofthe tests is high enough to involve transition on theblades, and both the freestream turbulence intensity(roughly 0.15%), the blade chord, collective pitch of 10degrees, and the surface roughness of the blade withrough grit over the leading edge up to quarter-chord,and the wooden surface aft of that, all contribute to thedevelopment of turbulent boundary layers. The seedparticles used are not monodisperse in size distribution,and some of them are expected to be in the regimewhere the spinout error must be considered. Except forthe tip Mach number, these are fairly realistic conditionsfor interpretation and application of the results, as willbe seen.IV. Experimental SetupThese experiments were conducted in Georgia Tech’sJohn Harper Wind Tunnel. The facility is a closedcircuit tunnel with a 2.13m x 2.74m test section. Airspeed is continuously variable up to 60 m/s. Turbulencelevels are 0.2%. The rotor shaft extends through the testsection ceiling to the centerline of the tunnel, and istilted forward by 6° to simulate forward flight. Attachedto this shaft is a two-bladed, teetering, untwisted,untapered, NACA 0015 rotor. The radius and bladechord are 9.457m and 85.7mm respectively. Testconditions for these experiments were a rotor RPM of1050 and an advance ratio of 0.10. An optical sensor isused to generate a TTL 1/rev pulse used for phaseaveraging measurements.Figure 1 - Forward flight experimental setupSingle velocity component measurements were madeusing a laser velocimeter (LV) on the advancing bladeside (ABS). The multi-line output from a 5W argon-ionlaser is used to power the laser Doppler velocimeter.The green line (514.5nm) is separated and then split intotwo beams, frequency shifted and coupled in to a fiberoptic probe in a TSI Colorburst module. The probe ismounted in the test section to a three-axis lineartraverse. The probe and traverse are well outside of therotor wake to minimize their effects on the rotor flowfield. All of these measurements were made inbackscatter mode. The measurement volume is ellipsoidwith a diameter of 90.5µm and a length of 1.31mm. Themeasurement grid consisted of a course grid with5.08mm steps and a finer grid centered on the blade-tipwith 2.54mm steps. The origin for these measurementsis located at the blade-tip trailing edge when ψ = 90°.One hundred thousand points were collected at eachmeasurement location. The data were phase averagedand then sorted by rotor azimuth into bins 0.5° wide.Figure 2 - ABS measurement gridMineral oil is used for the LV seeding. The seeder islocated downstream, so particles are drawn through 4turning vanes, the fan, honeycomb and screens beforeentering the test section. Particle diameter rangesbetween 1 and 5 µm. based on Multiple-Ratio Single-Particle sizing performed in the 1980s.Since previous work [19-20] has shown that theflowfield is periodic to within 1° of rotor azimuth, thethree-dimensional velocity field can be reconstructedfrom single velocity component measurements. Theability to reconstruct the flow field is vital to thesemeasurements, as the rotor interferes withmeasurements for certain azimuths at certain locations.To alleviate these problems, each velocity componentwas measured from two different probe orientations.The two resulting datasets had missing data for differentazimuths. The datasets were then combined to form onecomplete dataset.Copyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

V. Formulation of the Seed Particle DynamicsProblemRadial force due to the fluid rotation, and aerodynamicdrag are assumed to be the only forces acting on theparticle. Particles are assumed spherical. Aerodynamicdrag acting on the particle is obtained from Stokesrelationship. The particle at time t is shown in Figure 3.Y#Figure 3 – Particle at time trxvuVyy&x&! = " tThe angle φ is the rotation of the fluid and θ is the angleof particle lag behind the gas rotation. The vectors u andv are the X and Y components, respectively, of the gasvelocity V at the particle’s position. The particle’svelocity is represented by x& and y& . Summing theforces in the X and Y directions and assuming Stokesdrag results in:! FX= mx &= FX= 6"µ rVDragr X! FY= my &= FY= 6"µ rVrYDragwhere V r is the velocity relative to the particle. From thediagram it can easily be shown that the relative velocityof the particle is given by:andVrXVrYy= u ! x& = ! V ! x&rx= v ! y& = V ! y&rThe gas velocity was modeled assuming solid bodyrotation in the vortex core and then switched to apotential model outside of the vortex core. The resultingequations of motion are:XwhereV& x + !& x + ! y = 0rVy & + "& y ! " x = 0r& ,V ! o r"V18µ" =!2p d p= for 0 ! r ! Rco= for r > Rc2! rThe subscripts p and o represent the characteristics of theparticle and conditions at t = 0, respectively.These equations were numerically integrated usingMatlab software. Particles with diameters of 1.0, 2.0,3.0, 4.0 and 5.0 microns were examined. All particleswere “released” at r/R c = 0.01 with an angular velocityequal to that of the gas. The numerical integration wasstopped when r/R c = 3.0. Initial angular velocity, ω o ,vortex circulation, Γ o , and core radius were determinedfrom experimental data. These correspond to 3333 rad/s,0.754 m 2 /s and 0.006 m respectively. The Stokesnumbers for these particles based on the initial angularvelocity are listed in Table 1.ParticleDiameter(µm)Stokes Number =1 0.00882 0.03513 0.07894 0.14025 0.2191Table 1- Particle’s Stokes numbersVI. Results" ! Dpo18µVI.1 Nature of the Blade Tip FlowfieldThe blade tip flow field is complex and highly threedimensional.Mahalingam [18] found two significantfeatures in addition to the tip vortex. The first was asubstantial spanwise flow directed towards the tip onboth the upper and lower sides of the blade. Heobserved velocities approaching 40% of the tip-speedon the lower surface. The second feature was that thepeak axial velocity approached the tip-speed. Figure 4shows the measured axial velocities. At x/c = 0.45, theaxial velocity is 52% of the tip-speed. As themeasurement volume moves towards the trailing edge,the peak velocity levels off at 20% of the tip-speed. The2pCopyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

V z/ !Rfirst point at x/c = 0.36 is very close to the bladesurface. Scattering from the surface significantlydecreases the signal to noise ratio, therefore this point issuspect. If the first point is ignored, then the datasuggests that the axial velocity may reach the tip-speedduring formation.first chordwise station, it is 3% of the blade chord. Bythe time it reaches the trailing edge it has increased to9% of the chord.YZX0.80.20.60Va /! R0.4-0.2-0.40.200.4 0.6 0.8 1 1.2x/cFigure 4 - Axial velocity during formationSpanwise flows on the rotor blade have been reportedon before in the literature. Komerath et al [10] examinedthe blade tip flow field both while the blade wasspinning and in fixed wing mode. In the fixed wingmode, the tunnel freestream was adjusted to match thetip-speed of the rotating measurements. A substantialincrease in spanwise velocity was found in the rotarywing tests compared to fixed-wing mode tests.VI.2 Nature of the core as the vortex first formsFigure 5 shows distinct circumferential velocity profilesduring formation. The first clear circumferentialvelocity profile occurs at a value of x/c of 0.47. In thisprofile there is a distinct region of solid body rotation.The region outside of the “core” does not decay at the1/r rate normally seen in vortices. This behaviorcontinues to a chordwise location of 0.55, beyond whichdecay proportional to 1/r develops on the inboard sideof the vortex. The outboard side of the vortex does notexhibit this behavior until x/c of 0.72. Kinks in thevelocity profiles are also observed at some chordwisestations. This suggests that the formation process mayinvolve discrete structures rolling up around the core.VI.3 Evolution of vortex circulation over the blade tipAt the first chordwise station with a distinctcircumferential velocity profile, x/c = 0.47, the vortexstrength is 0.19m 2 /s. Towards the trailing edge thevortex strength increases to 0.92 m 2 /s, as seen in Figure6. This suggests that formation processes may involvethe rolling up of vortex filaments. The core radius alsoincreases as one moves toward the trailing edge. At the-0.60.20.0y/c-0.20.500.751.001.25Figure 5 - Circumferential velocity profiles duringformation! (m 2 /s)10.90.80.70.60.50.40.30.20.1000.5 0.6 0.7 0.8 0.9 1x/cx/c! (m 2 /s)r/c0.150.10.05Figure 6 - Evolution of the vortex strength and coreradiusIt should be noted that some of the length scales of thevortex are near the resolution of the LV system. At thetrailing edge, the vortex is large enough so that there arenine measurement points in the core. However, at thefirst discernable velocity profile, there are only threemeasurement points across the core. Closer to theleading edge, the scales should be even smaller. Thisexplains why no obvious formation was observedforward of this point.0.2r/CCopyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

VI.4 Wake Evolution to 540 degreesData on the tip vortex generated with the blade at 4positions are shown in Figures 7 & 8: the AdvancingBlade Side (ABS; Ψ = 90°), the front of the rotor (Ψ =180°, the Retreating Blade Side (Ψ=27°) and the rear ofthe rotor (Ψ = 0°). Trends in the measured peakcircumferential velocity at all four locations are similar– they start out at approximately 40% of tip-speed andslowly decay to roughly 20%, before leveling off.Velocities on the ABS and rear are approximately 10%lower than at the other stations. On the ABS (Figure 7),the peak circumferential velocity starts out at about 35%of the tip-speed. This value is consistent with themeasurements on the formation of the vortex. There is agradual decay to a vortex age of 150° where it levels outto approximately 20% of the tip-speed. The velocityremains at 20% of tip-speed until a vortex age of 200°.The measurements after 200° are from a second tunnelentry. These measurements show a peak circumferentialvelocity of 25% of tip-speed out to a vortex age of 488°.The reason for this discontinuity is not clear.0.80.70.6Recall from the vortex formation measurements that thecore radius at the trailing edge was 9% of the chord. Thereason for this discrepancy is not yet known; furtheranalysis of the data is still needed. However, onepossible explanation is that the vortex may not becompletely rolled up. It may take several chord lengthsfor the vortex to completely form.VC /(! R)0.80.70.60.50.40.30.20.1RBSFrontRear00 20 40 60 80 100 120vortex age ( degrees )Figure 8 - Evolution of peak circumferential velocityVC /(! R)0.50.40.150.30.20.100 75 150 225 300 375 450vortex age ( degrees )Figure 7 - Evolution of peak circumferential velocityon the ABSOn the RBS (Figure 8), the circumferential velocitypeaks at 45% of the tip-speed, and then decays to 30%of the tip-speed by a vortex age of 50°. The front andrear of the rotor also demonstrate similar trends.On the RBS and the front of the rotor, the core radiusvaries between 6% and 7% of the chord (Figure 9). Atrear of the rotor, the radius increases from 4% of thechord to 6% by an age of 72°, and then decreases backto 4% at age of 108°. One the ABS, there is an increasefrom 5.5% to 6.5% between 24° and 36° of vortex agefollowed by decay to 4.5% at age of 96°(Figure 10).For vortex ages between 189° and 488° the radiusoscillates between 4 and 7% of the chord.core radius ( non-dim. by chord )0.10.0500 24 48 72 96vortex age ( degrees )Figure 9 - Evolution of the core radiusRBSFrontRearThe wake boundaries are shown in Figure 11 and Figure12. On the ABS and RBS, the boundaries aredominated by contraction. In the far wake on the ABS,the boundary exhibits a slight change of slope at z/R of–0.30. The boundaries at the front and rear of the rotorare dominated by convection.Copyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

core radius ( non-dim. by chord )0.150.10.0500 60 120 180 240 300 360 420 480 540vortex age ( degrees )Figure 10 - Evolution of the core radius on the ABSVI.5 Periodic Fluctuations in Core Axial VelocityThe evolution of the peak axial velocity is shown inFigure 13. The data from the front of the rotor has beenremoved for clarity. On the ABS, the peak velocitystarts at a little over 20% of the tip-speed and rapidlyincreases to nearly 60% of the tip-speed. This behavioris then followed by a gradual decay back down to 20%of the tip-speed by a vortex age of 160°. The rear of therotor shows peak decaying from 22% of the tip-speed to8% 108° of vortex age. On the RBS, the peak axialvelocity reaches nearly 80% of the tip-speed. A sharpdrop follows this peak to 23% of the tip-speed by 5° ofvortex age. After that point, it exhibits harmonicoscillations. Inspection of the other velocities shows thesame oscillations. The period of this oscillation is nearly10° of rotor azimuth. This corresponds to a Strouhalnumber, based on blade tip thickness, of 0.16.0.00RBSABS-0.05-0.10z/R-0.15-0.20-0.25-0.30Rear view-0.35-0.40-1 -0.5 0 0.5 1y/RFigure 11 – Wake boundaries on the ABS and RBS0.04rear0-0.04z/R-0.08-0.12-0.16frontView from the RBS-1 -0.5 0 0.5 1x/RFigure 12 – Wake boundaries on the front and rearVa /(! R)0.80.60.40.2Strouhal No. = 0.16ABSRBSRear00 48 96 144vortex age ( degrees )Figure 13 - Evolution of the peak axial velocity (frontstation removed for clarity)Another interesting feature of Figure 13 is the axialvelocity on the RBS reaching nearly 80% of the tipspeed.The magnitude of this velocity alludes to thepeak axial velocity reaching tip-speed during formationperhaps due to the no-slip boundary condition. Seedparticle dynamics may explain why velocities of thismagnitude are not observed at the other stations. On theRBS the blade and freestream directions are the same.Therefore the velocity difference between seed particlesin the freestream and the local fluid velocity around theblade is much smaller than at the other stations. As aresult, the seed particles can more quickly adjust to thelocal fluid velocity. Measurements were made to extendthe data on the evolution of the axial velocity out tovortex age of 540°. By a vortex age of 160° the numberof data points inside the vortex core had diminished tothe point that no conclusion could be made on the peakaxial velocity.Copyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

VI. 8 Accuracy of the SimulationThe Stokes relationship used for particle drag wasdeveloped under the assumption that the Reynoldsnumber, based on the particle relative velocity anddiameter, is less than 1. The Reynolds number of theparticles as they are centrifuged from the core is shownin Figure 18. According to Dring [23], for Re p > 1,Stokes relationship tends to under predict drag.Figure 19 compares C D predicted by Stokes relationshipand the drag models used by Dring. Stokes relationshipunder-predicts drag by 50% for the largest particles nearthe edge of the core. This under-prediction of the dragmeans that the trajectories and velocity errors areconservative estimates.302520CD15105Stokes RelationExperimental Curve Fit [23]2 4 6 8 10R epFigure 19 - Comparison of drag predictionsAs the tip speed increases, the vortex strength increasesrapidly, so that smaller particles would be needed tokeep the level of error low. However, the Reynoldsnumber of the relative flow might also increase, makingthe Stokes flow simulation less accurate. As mentionedpreviously, and as shown by comparison with the coresize measurements, the axial velocity in the core shouldalso be considered to perform a useful simulation ofseed particle dynamics in rotor tip vortices.VII. ConclusionsThis paper discussed experiments performed to gain afundamental understanding of the physics of the tipvortex formation process on a rotor blade in forwardflight. The discussion also addressed simulations used toquantify the errors due to seed particle dynamics in aprevious set of LDV measurements of near-wake vortexproperties.VII.1 Vortex Formation1. Strong spanwise velocities occur on the upper andlower surfaces of the blade near the tip, unlike inthe case of fixed wings.2. The vortex formation process was observed startingat a chordwise location of 0.47. Length scalessmaller than the resolution of the LDV systemprobably prevented the observation of theformation process closer to the leading edge.3. Vortex strength was seen to increase from 0.19m 2 /sat x/c = 0.47 to 0.89m 2 /s at the trailing edge. Anincrease in radius from 3% to 9% of the chord wasalso observed over the same interval.4. The early velocity profiles clearly show a core ofsolid body rotation, but do not show a 1/r decayoutside of the core. The 1/r decay occurs later,starting on the inboard side of the vortex and laterdeveloping on the outboard side.5. Kinks in the velocity profiles suggest that theformation process may be due to discrete vortexfilaments rolling up into the tip vortex.VII.2 Vortex Evolution in the Wake1. The tip vortex core size remains essentiallyconstant upto a vortex age of 450 degrees.2. The peak circulatory velocity decays byapproximately 30 percent in the first 150 degreesand thereafter remains constant to 450 degrees.3. Periodic fluctuations are observed in the core axialvelocity in the near wake.VII.3 Near Wake Seed Particle Dynamics1. For a vortex representative of that found in theexperiments of References 1 – 2, errors in thecircumferential velocity up to 8% for the largestparticle size were estimated.2. The rotation of the fluid also imparted a radialvelocity up to 20% of the circumferential velocity.3. Comparison with the measured core size shows thatthe seed particle spinout predictions are extremelyconservative.4. Based on the above reasoning, it is seen that theactual magnitude of error in the core tangentialvelocity due to seed particle spinout is negligible.5. Stokes drag predictions under estimated the dragacting on the particles near the edge of the core; thevelocity error and particle trajectories are thereforeconservative estimates.6. Predictions of seed particle dynamics for rotor tipvortices should incorporate the substantial effectsof core axial velocity, and proper models forparticle drag appropriate for the actual Reynoldsnumber range.Copyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001

VIII AcknowledgementsThis work was performed under a sub-grant from theOhio State Foundation as part of a grant from the ArmyResearch Office. Dr. Thomas Doligalski is the AROTechnical Monitor, and Prof. A. Terry Conlisk is theOSU Principal Investigator. The authors acknowledgethe assistance of Dr. Raghav Mahalingam in this work .IX References1. Mahalingam, R., “Structure of the Near Wake of aRotor in Forward Flight and Its Effect on SurfaceInteractions”, Ph.D. Thesis, Georgia Institute ofTechnology, June 1999.2. Wong, O.D., Mahalingam, R., Tongchitpakdee, C.,Komerath, N.M., “The Near Wake Of A 2-BladedRotor In Forward Flight”, AHS AeromechanicsSpecialists Meeting, Atlanta, GA, November 2000.3. Thompson, T.L., Komerath, N.M., and Gray, R.B.,"Visualization and Measurement of the Tip VortexCore of a Rotor Blade in Hover". Journal ofAircraft, Vol. 25, No. 12, Dec. ‘88, pp. 1113 - 21.4. Komerath, N.M., Liou, S.G., Thompson, T.L., "ARemote-Aligned Off-Axis Receiving System forLaser Velocimetry in Large Facilities”.Experimental Techniques. 14, 4, July 90, 29-33.5. Brand, A.G., Komerath, N.M., and McMahon,H.M., "Results from the Laser Sheet Visualizationof an Incompressible Vortex Wake". Journal ofAircraft, Vol. 26, No. 5, May 1989, pp. 438-443.6. Brand, A.G., McMahon, H.M., and Komerath,N.M. "Correlations of Rotor/Wake - AirframeInteractions with Flow Visualization Data". Journalof the American Helicopter Society. Vol. 35, No. 4,October 1990, p. 4-15.7. Liou, S.G., Komerath, N.M., and McMahon, H.M.,"Velocity Measurements of Airframe Effects on aRotor in Low-Speed Forward Flight". Journal ofAircraft, Vol 26, No. 4, April 1989, pp. 340 - 348.8. Liou, S.G., Komerath, N.M., McMahon, H.M.,"TheVelocity Field of a Circular Cylinder in the Wakeof a Rotor in Forward Flight". Journal Aircraft, 27,9, Sep.1990, p.804-809.9. Liou, S.G., Komerath, N.M., and McMahon, H.M.,"Measurement of Transient Vortex-SurfaceInteraction Phenomena". AIAA Journal, Vol, 28,No. 6, June 1990, p. 975-981.10. Komerath, N.M., Liou, S-G., Hyun, J-S.,"Flowfield of a Swept Blade Tip at High PitchAngles". AIAA 91-0704, Meeting, Jan. '91.11. Funk, R.B., Komerath, N.M., "Rotor WakeInteraction with a Lifting Surface". Proceedings ofthe American Helicopter Society Annual Forum, Ft.Worth, TX, May 1995.12. Caradonna, F., Henley, E., Silva, M., Huang, S.,Komerath, N.M., Reddy, U., Mahalingam, R.,Funk, R., Wong, O., Ames, R., Darden, L.,Villareal, L., Gregory, J., "An Experimental Studyof a Rotor in Axial Flight". AHS Specialists'Meeting on Rotorcraft Aerodynamics andAeroacoustics, Williamsburg, VA, October 1997.13. Caradonna, F., Henley, E., Silva, M., Huang, S.,Komerath, N.M., Reddy, U., Mahalingam, R.,Funk, R., Wong, O., Ames, R., Darden, L.,Villareal, L., Gregory, J., "PerformanceMeasurements and Wake Characteristics of aModel Rotor in Axial Flight". AHS Journal, Oct.99.14. McAlister, K.W., “Measurements in the Near Wakeof a Hovering Rotor”, AIAA 96-1958, FluidDynamics Conference, June 1996.15. McAlister, K.W., Schuler, C.A., Branum, L., Wu,J.C., "3-D Measurements Near a Hovering Rotorfor Determining Profile and Induced Drag", NASATP 3577, ATCOM Technical Report 95-A-006.16. Leishman, J.G., Baker, A., Coyne, A.,"Measurement of Rotor Tip Vortices Using Three-Component Laser Doppler Velocimetry", AHSAeromechanics Specialists Conference, Oct.1995.17. Jain, R., Conlisk, A.T., ``Interaction of Tip-Vortices in the Wake of a Two-Bladed Rotor inAxial Flight'', Journal of the American HelicopterSociety, no. 3, July 2000, pp. 157-164.18. Mahalingam, R., Wong, O.D., Komerath, N.M.,“Experiments on the Origins of Tip-Vortices”,AIAA Paper 2000-0278, Reno, NV, January 2000.19. Mahalingam, R., Komerath, N.M., “Measurementsof the Near Wake of a Rotor in Forward Flight”,AIAA 98-0692, January 1998.20. Mahalingam, R., Komerath, N.M.,“Characterization of the Near Wake of aHelicopter”, AIAA 98-2909, Fluid DynamicsConference, June 1998.21. Dring, R.P., Casper, J.R., Suo, M., “ParticleTrajectories in Turbine Cascades”, Journal ofEnergy, Vol. 3, No. 3, May-June 1979, pp. 161-6.22. Dring, R.P., “Sizing Criteria for Laser AnemometryParticles”, Journal of Fluids Engineering, Vol. 104,March 1982, pp. 15-17.23. Dring, R.P., Suo, M., “Particle Trajectories inSwirling Flows”, Journal of Energy, Vol. 2, No. 4,July-August 1978, pp. 232-237.24. Kriebel, A.R., “Particle Trajectories in a GasCentrifuge”, Journal of Basic Engineering, Vol. 83,No. 3, September 1961, pp. 333-340.25. Leishman, J.G., “Seed Particle Dynamics in TipVortex Flows”, Journal of Aircraft, Vol. 33, No. 4,July-August 1996, pp. 823-825.26. Komerath, N.M., Thompson, T.L., Kwon, O.J., andGray, R.B., "The Velocity Field of a Lifting ModelRotor Blade in Hover". Journal of Aircraft, Vol.25, No.3, March 1988, pp. 250 - 257.Copyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001